[backport 2.3.x] TST(string dtype): Resolve xfail when grouping by nan column (#60712) (#60719)

TST(string dtype): Resolve xfail when grouping by nan column (#60712)

(cherry picked from commit 55a6d0a)

Author: rhshadrach

pandas/tests/groupby/test_groupby.py

@@ -6,8 +6,6 @@
 import numpy as np
 import pytest
 
-from pandas._config import using_string_dtype
-
 from pandas.errors import (
     PerformanceWarning,
     SpecificationError,
@@ -2876,12 +2874,13 @@ def test_groupby_none_in_first_mi_level():
     tm.assert_series_equal(result, expected)
 
 
-@pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
-def test_groupby_none_column_name():
+def test_groupby_none_column_name(using_infer_string):
     # GH#47348
     df = DataFrame({None: [1, 1, 2, 2], "b": [1, 1, 2, 3], "c": [4, 5, 6, 7]})
-    result = df.groupby(by=[None]).sum()
-    expected = DataFrame({"b": [2, 5], "c": [9, 13]}, index=Index([1, 2], name=None))
+    by = [np.nan] if using_infer_string else [None]
+    gb = df.groupby(by=by)
+    result = gb.sum()
+    expected = DataFrame({"b": [2, 5], "c": [9, 13]}, index=Index([1, 2], name=by[0]))
     tm.assert_frame_equal(result, expected)